Canon’s Zoombrowser EX version 6.0 is truly color-managed as far as I can tell, means that the monitor profile is used for conversion and display on screen. Probably there’s a free download somewhere in the support section for their cameras. IF you shoot with a Canon, Raw files are previewed as well, while emulating the in-camera flavor of conversion. There’s a full screen mode, although it is to mention that the software is slow in many aspects.

Windowz’ Picture & Fax viewer as well as their Raw viewer power tool like to convert everything to sRGB for monitor output (at least when I tried the last time), so that there’s easily a discrepancy with a monitor’s de facto given gamut.

I use IrfanView on a PC. It doesn't have any negative color issues that I'm aware of. It's free, it has a one-key toggle between full screen and normal, one-key toggle for full size, one key for image info, settings for how full screen is expressed for images larger and smaller than the screen, view by filename or date etc., and much more.

When I go to "Options" under this program, should I turn the profile to "off", or should I turn it to the calibrated profile that I am currently using for my monitor? If I do the latter, wouldn't I be using this profile "twice"?

[...] should I turn it to the calibrated profile that I am currently using for my monitor?

Yes, just check the box and select your monitor profile in the list. The conversion is not performed twice as nothing really happens when you set a monitor profile in control panel. This is just a place where applications can go look for your preferences (and you can put multiple profiles in there, by the way), but the actual conversion really is handled by the applications. Now, if you use some special software that loads with Windows and runs at all times to "color manage" your desktop, you might want to make some tests. You could use Photoshop as reference, and you should get exactly the same rendition in FPV if everything is working and set as it should.

You can get small images with esoteric profiles from this page (ICC website), just right-click and save them, they are useful to find out if CM is working as it should with any app.